The Red Sox finish one big American League East series against the Rays on Thursday night before beginning one against the Yankees this weekend at Fenway Park. If they can get one more game off the Rays at The Trop, they will go into the Yankees series still in first place in the East. It means they are still far and away the biggest surprise of the AL season, every bit the surprise as the Giants have been in their league.

And what the Red Sox are really dreaming about doing is being the kind of surprise, all the way to the finish, that the 2013 Red Sox were. They aren’t as deep enough or talented as the ’18 Sox, the best team in Red Sox history, winning 108 regular-season games on their way to winning it all.

But it was the ’13 team that came into that season with expectations as low as they were coming into this season. Those Boston Red Sox had finished last the season before and gotten their manager Bobby Valentine fired after just one year. They still had David Ortiz in the middle of the order, but around him, they had grinders like Shane Victorino and Mike Napoli and Jonny Gomes. And they ended up beating the Rays and the Yankees in the East, which is what they’re trying to do again, before they finally won it all.

Can this team win the East? We’re going to find out over the last three months of the ’21 season. But no one in this world expected them to be where they are going into the last game of the current Rays series, a half-game in front of them, carrying the second-best record in the American League (after a crazy hot Astros team) and somehow still tied for having the third best in baseball. And that is after starting their season by getting swept by the Orioles at Fenway.

On Tuesday night, they found a way to beat the Rays, 9-5, in 11 innings, the same kind of crazy extra-inning win they got off Tampa Bay after that Orioles series in April, as they were only just beginning to come back from 0-3 by winning nine games in a row.

Here is what Alex Cora said about his team after Tuesday’s game:

“If you take a look at the guys that we have on this roster, they have to earn everything they have. We’ve got a bunch of grinders, a bunch of guy that on other teams they didn’t play that much. They’re getting the opportunity to play here. We just like to play baseball. It’s a good baseball team. ... We will push until the end.”

You look at the Red Sox and still wonder how a starting-pitching staff that has looked more than somewhat frayed lately can stand up over the second half of the season, no one knowing for sure when their ace, Chris Sale, will return from his Tommy John surgery last year. Even the guy who is their ace for now, Nathan Eovaldi, has had an up-and-down year on his way to a 7-4 record with a 3.90 ERA. He will pitch against the Yankees this weekend. But in his last start, he got hit hard by the Royals in Kansas City.

The Sox still are where they are, as Cora -- coming off a year’s suspension for his role in the Astros’ illegal sign-stealing when he was A.J. Hinch’s bench coach in Houston -- has reminded everyone what a gifted manager he still is, three years after his ’18 team won the Series, beating the Astros along the way. And somehow he has found enough grinders to fit in around J.D. Martinez and Xander Bogaerts and Rafael Devers in the middle of his batting order.

When the Sox came back from an early 2-0 deficit against the Rays on Tuesday, it was their 25th come-from-behind victory this season, the most in baseball. It made them 4-0 against the Rays this season, until Tampa Bay got them 8-2 the next night behind Rich Hill.

The good news is that they are in play again, in a season when people had a right to think they might only finish ahead of the Orioles in the East. The grinders this time are named Christian Arroyo and Enrique Hernández and Marwin Gonzalez and Hunter Renfroe. They have starting pitchers named Garrett Richards, who has seen his spin rate plummeting the way the Dow sometimes has lately, and Martín Pérez and Nick Pivetta.

Cora’s Red Sox don’t stay down for long when they get hit. The Blue Jays got them for 18 runs at Fenway, and the Sox came back the next day to win and split a four-game series. Now they’ve got the Yankees, whom they swept earlier in the month at Yankee Stadium, and who are showing signs of life. The Rays never go away. The Blue Jays are lurking in fourth place in a division that looks as if it will be a grind the rest of the way.

Can the Red Sox go from last to first again? Who knows? But off the season they’ve played, and watching the way they keep coming back, it’s going to be fun watching them try.